An own goal from Fleetwood and a strike from Reece Webb-Foster in the second period at the Cod Army's Poolfoot Farm training ground saw City claim the win in the second-string match.
Webb-Foster was introduced at the interval after Thomas played the first half of the reserve game. Davies featured for 68 minutes while Evans was given 89 minutes.
Goalkeeper Joe Cracknell and winger Dylan Mottley-Henry played the whole match.
City's victory in the tie means that the Bantams finish second in Northern Group A of the Final Third Development League Cup behind group winners Burnley, who now progress to the semi-finals.
The club's next reserve game is a Final Third Development League fixture scheduled for this coming Tuesday (9 February 2016) at home to Shrewsbury Town.
CITY XI
1. Joe Cracknell
2. Kwame Boateng
3. Tom Windle
4. Lee Evans
5. Kesi Omolokun
6. Luca Mellor
7. Dylan Mottley-Henry
8. Sumaili Cissa
9. Steven Davies
10. Wes Thomas
11. Ellis Hudson
Substitutes:
12. Chandler Hallwood
14. Reece Webb-Foster
15. Niah Payne
Substitutions:
Webb-Foster for Thomas (46), Payne for Davies (68), Hallwood for Evans (89)